Methods of obtaining ophthalmic lenses providing the eye with reduced aberrations

ABSTRACT

The present invention discloses methods of obtaining ophthalmic lens capable of reducing the aberrations of the eye comprising the steps of characterizing at least one corneal surface as a mathematical model, calculating the resulting aberrations of said corneal surface(s) by employing said mathematical model, selecting the optical power of the intraocular lens. From this information, an ophthalmic lens is modeled so a wavefront arriving from an optical system comprising said lens and corneal model obtains reduced aberrations in the eye. Also disclosed are ophthalmic lenses as obtained by the methods which are capable reducing aberrations of the eye.

FIELD OF INVENTION

[0001] The present invention relates to methods of designing ophthalmiclenses that provide the eye with reduced aberrations, as well as lensescapable of providing such visual improvements.

BACKGROUND OF THE INVENTION

[0002] It is presently discussed that the visual quality of eyes havingan implanted intraocular lens (IOL) is comparable with normal eyes in apopulation of the same age. Consequently, a 70 year old cataract patientcan only expect to obtain the visual quality of a non-cataracteousperson of the same age after surgical implantation of an intraocularlens, although such lenses objectively have been regarded as opticallysuperior to the natural crystalline lens. This result is likely to beexplained by the fact that present IOLs are not adapted to compensatefor defects of the optical system of the human eye, namely opticalaberrations. Age-related defects of the eye have recently beeninvestigated and it is found that contrast sensitivity significantlydeclines in subjects older than 50 years. These results seem to complywith the above-mentioned discussion, since the contrast sensitivitymeasurements indicate that individuals having undergone cataract surgerywith lens implantation lens will not obtain a better contrastsensitivity than non-cataracteous persons of an average age of about 60to 70 years.

[0003] Even if intraocular lenses aimed at substituting the defectivecataract lens and other ophthalmic lenses, such as conventional contactlenses, have been developed with excellent optical quality as isolatedelements, it is obvious that they fail to correct for a number ofaberration phenomena of the eye including age-related aberrationdefects.

[0004] U.S. Pat. No. 5,777,719 (Williams et al.) discloses a method andan apparatus for accurately measuring higher order aberrations of theeye as an optical system with wavefront analysis. By using aHartmann-Shack wavefront sensor, it is possible to measure higher orderaberrations of the eye and use such data to find compensation for theseaberrations and thereby obtain sufficient information for the design ofan optical lens, which can provide a highly improved opticalperformance. The Hartmann-Shack sensor provides means for analyzinglight reflected from a point on the retina of the eye of a subject. Thewavefront in the plane of the pupil is recreated in the plane of thelenslet array of the Hartmann-Shack sensor. Each lenslet in the array isused to form an aerial image of the retinal point source on a CCD cameralocated at the focal plane of the array. The wave aberration of the eye,in the form resulting from a point source produced on the retina by alaser beam, displaces each spot by an amount proportional to the localslope of the wavefront at each of the lenslets. The output from the CCDcamera is sent to a computer, which then performs calculations to fitslope data to the first derivatives of 66 Zernike polynomials. Fromthese calculations, coefficients for weighting the Zernike polynomialsare obtained. The sum of the weighted Zernike polynomials represents areconstructed wavefront distorted by the aberrations of the eye as anoptical system. The individual Zernike polynomial terms will thenrepresent different modes of aberration.

[0005] U.S. Pat. No. 5,050,981 (Roffman) discloses another method fordesigning a lens by calculating modulation transfer functions fromtracing a large number of rays through the lens-eye system andevaluating the distribution density of the rays in the image position.This is repeatedly performed by varying at least one lens surface untila lens is found which results in a sharp focus and a maximum modulationtransfer function.

[0006] U.S. Pat. No. 6,224,211 (Gordon) describes a method of improvingthe visual acuity of the human eye by successively fitting asphericlenses to the cornea and thereby finding a lens that can reducespherical aberration of the whole individual eye.

[0007] The methods referred to above for designing are suitable for thedesign of contact lenses or other correction lenses for the phakic eyewhich can be perfected to compensate for the aberration of the whole eyesystem. However, to provide improved intraocular lenses aimed to replacethe natural crystalline lens, it would be necessary to consider theaberrations of the individual parts of the eye.

[0008] U.S. Pat. No. 6,050,687 (Bille et al) refers to a method whereinthe refractive properties of the eye are measured and whereinconsideration is taken to the contribution of the individual surfaces ofthe eye to the total wavefront aberrations. The method described hereinparticularly aims at analyzing the topography of the posterior cornealsurface in order to improve refractive correction techniques.

[0009] There has recently been a focus on studying the aberrations ofthe eye, including a number of studies of the development of theseaberrations as a function of age. In two particular studies, thedevelopment of the components of the eye were examined separately,leading to the conclusion that the optical aberrations of the individualcomponents of younger eyes cancel each other out, see Optical Letters,1998, Vol. 23(21), pp.1713-1715 and IOVS, 2000, Vol.41(4), 545. Thearticle of S. Patel et al in Refractive & Corneal Surgery, 1993, Vol. 9,pages 173-181 discloses the asphericity of posterior corneal surfaces.It is suggested that the corneal data can be used together with otherocular parameters to predict the power and the asphericity of anintraocular lens with the purpose of maximizing the optical performancesof the future pseudophakic eye. Furthermore, it was also recentlyobserved by Antonio Guirao and Pablo Artal in IOVS, 1999, Vol. 40(4),S535 that the shape of the cornea changes with age and becomes morespherical. These studies indicate that the cornea in the subjectsprovides a positive spherical aberration, which increases slightly withthe age. On the other hand, the rotationally symmetric aberration of theanterior corneal surface does not seem to be different between youngerand older eye according to results found by T Oshika et al inInvestigative Ophthalmology and Visual Science, 1999, Vol. 40, pp.1351-1355. In Vision Research, 1998, 38(2), pp. 209-229, A Glasser etal. investigated the spherical aberration of natural crystalline lensesfrom eyes obtained from an eye bank after the cornea has been removed.According to the laser scanner optical method used herein it was foundthat the spherical aberration from an older lens (66 years) showspositive spherical aberration, whereas a 10-year-old lens shows negativespherical aberration. In addition, Vision Research, 2001, 41, pp.235-243(G Smith et al) discloses that the natural crystalline lens appears tohave negative spherical aberration when in the relaxed state. Smith etal suggest that because older eyes have a larger aberration, it islikely that the spherical aberration of the crystalline lens becomesless negative with age.

[0010] In Ophthal. Physiol. Opt., 1991, Vol. 11, pp. 137-143 (DAAtchison) it is discussed how to reduce spherical aberrations inintraocular lenses by aspherizing the lens surface. The methods outlinedby Atchison are based on geometric transferring calculations, which donot consider diffraction effects and any variations in refractive indexalong the ray path in inhomogeneous elements. These calculations willlead to errors close to the diffraction limit. Also in WO 98/31299(Technomed) a ray tracing method is outlined according to which therefraction of the cornea is attempted to be considered for the design ofan intraocular lens. In view of the foregoing, it is apparent that thereis a need for ophthalmic lenses that are better adapted or compensatedto the aberrations of the individual surfaces of the eye and are capableof better correcting aberrations other than defocus and astigmatism, asprovided by conventional ophthalmic lenses.

DESCRIPTION OF THE INVENTION

[0011] It is an object of the invention to provide for methods thatresult in obtaining an ophthalmic lens, which provides the eye withreduced aberrations.

[0012] It is another object of the invention to provide methods ofobtaining an intraocular lens capable of reducing the aberration of theeye after its implantation into the eye.

[0013] It is a further object to provide for methods of obtaining anintraocular lens capable of compensating the aberrations resulting fromoptical irregularities in the corneal surfaces.

[0014] It is a still further object of the present invention to providean intraocular lens which is capable of restoring a wavefront deviatingfrom sphericity into a substantially more spherical wavefront.

[0015] It is a also an object of the present invention to provide anintraocular lens which is capable of correcting for mean opticalirregularities and imperfections found in a particular group of peopleand thereby provide a lens with improved optical performance for anindividual belonging to the same group.

[0016] The present invention generally relates to an ophthalmic lens andto methods of obtaining said ophthalmic lens that is capable of reducingthe aberrations of the eye. By aberrations in this context is meantwavefront aberrations. This is based on the understanding that aconverging wavefront must be perfectly spherical to form a point image,i.e. if a perfect image shall be formed on the retina of the eye, thewavefront having passed the optical surfaces of the eye, such as thecornea and a natural or artificial lens, must be perfectly spherical. Anaberrated image will be formed if the wavefront deviates from beingspherical. In this context the term nonspherical surface will refer torotationally symmetric, asymmetric and/or irregular surfaces, i.e. allsurfaces differing from a sphere. The wavefront aberrations can beexpressed in mathematical terms in accordance with different approximatemodels as is explained in textbook references, such as M. R. Freeman,Optics, Tenth Edition, 1990.

[0017] In a first embodiment, the present invention is directed to amethod of designing an intraocular lens capable of reducing aberrationsof the eye after its implantation. The method comprises a first step ofcharacterizing at least one corneal surface as a mathematical model andby employing the mathematical model calculating the resultingaberrations of the corneal surface. An expression of the cornealaberrations is thereby obtained, i.e. the wavefront aberrations of aspherical wavefront having passed such a corneal surface. Dependent onthe selected mathematical model different routes to calculate thecorneal aberrations can be taken. Preferably, the corneal surface ischaracterized as a mathematical model in terms of a conoid of rotationor in terms of polynomials or a combination thereof. More preferably,the corneal surface is characterized in terms of a linear combination ofpolynomials. The second step of the method is to select the power of theintraocular lens, which is done according to conventional methods forthe specific need of optical correction of the eye, for example themethod described in U.S. Pat. No. 5,968,095 From the information ofsteps one and two an intraocular lens is modeled, such that a wavefrontfrom an optical system comprising said lens and corneal model obtainsreduced aberrations. The optical system considered when modeling thelens typically includes the cornea and said lens, but in the specificcase it can also include other optical elements including the lenses ofspectacles, or an artificial correction lens, such as a contact lens, acorneal inlay implant or an implantable correction lens depending on theindividual situation.

[0018] Modeling the lens involves selection of one or several lensparameters in a system which contributes to determine the lens shape ofa given, pre-selected refractive power. This typically involves theselection of the anterior radius and surface shape, posterior radius andsurface shape, the lens thickness and the refractive index of the lens.In practical terms, the lens modeling can be performed with data basedon a conventional spherical lens, such as the CeeOn® lenses fromPharmacia Corp., as exemplified with the CeeOn® Edge (Model 911). Insuch a case, it is preferred to deviate as little as possible from analready clinically approved model. For this reason, it may be preferredto maintain pre-determined values of the central radii of the lens, itsthickness and refractive index, while selecting a different shape of theanterior and/or posterior surface, thus providing one or both of thesesurfaces to have an nonspherical shape. According to an alternative ofthe inventive method, the spherical anterior surface of the conventionalstarting lens is modeled by selecting a suitable aspheric component.Preferably the lens has at least one surface described as a nonsphere orother conoid of rotation. Designing nonspherical surfaces of lenses is awell-known technique and can be performed according to differentprinciples and the description of such surfaces is explained in moredetail in our parallel Swedish Patent Application 0000611-4 to which isgiven reference.

[0019] The inventive method can be further developed by comparingwavefront aberrations of an optical system comprising the lens and themodel of the average cornea with the wavefront aberrations of theaverage cornea and evaluating if a sufficient reduction in wavefrontaberrations is obtained. Suitable variable parameters are found amongthe above-mentioned physical parameters of the lens, which can bealtered so as to find a lens model, which deviates sufficiently frombeing a spherical lens to compensate for the corneal aberrations.

[0020] The characterization of at least one corneal surface as amathematical model and thereby establishing a corneal model expressingthe corneal wavefront aberrations is preferably performed by directcorneal surface measurements according to well-known topographicalmeasurement methods which serve to express the surface irregularities ofthe cornea in a quantifiable model that can be used with the inventivemethod. Corneal measurements for this purpose can be performed by theORBSCAN® videokeratograph, as available from Orbtech, or by cornealtopography methods, such as EyeSys® from Premier Laser Systems.Preferably, at least the front corneal surface is measured and morepreferably both front and rear corneal surfaces are measured andcharacterized and expressed together in resulting wavefront aberrationterms, such as a linear combination of polynomials which represent thetotal corneal wavefront aberrations. According to one important aspectof the present invention, characterization of corneas is conducted on aselected population with the purpose of expressing an average of cornealwavefront aberrations and designing a lens from such averagedaberrations. Average corneal wavefront aberration terms of thepopulation can then be calculated, for example as an average linearcombination of polynomials and used in the lens design method. Thisaspect includes selecting different relevant populations, for example inage groups, to generate suitable average corneal surfaces.Advantageously, lenses can thereby be provided which are adapted to anaverage cornea of a population relevant for an individual elected toundergo cataract surgery or refractive correction surgery includingimplantation of an IOL or corneal inlays. The patient will therebyobtain a lens that gives the eye substantially less aberrations whencompared to a conventional spherical lens.

[0021] Preferably, the mentioned corneal measurements also include themeasurement of the corneal refractive power. The power of the cornea andthe axial eye length are typically considered for the selection of thelens power in the inventive design method.

[0022] Also preferably, the wavefront aberrations herein are expressedas a linear combination of polynomials and the optical system comprisingthe corneal model and modeled intraocular lens provides for a wavefronthaving obtained a substantial reduction in aberrations, as expressed byone or more such polynomial terms. In the art of optics, several typesof polynomials are available to skilled persons for describingaberrations. Suitably, the polynomials are Seidel or Zernikepolynomials. According to the present invention Zernike polynomialspreferably are employed.

[0023] The technique of employing Zernike terms to describe wavefrontaberrations originating from optical surfaces deviating from beingperfectly spherical is a state of the art technique and can be employedfor example with a Hartmann-Shack sensor as outlined in J. Opt. Soc.Am., 1994, Vol. 11(7), pp. 1949-57. It is also well established amongoptical practitioners that the different Zernike terms signify differentaberration phenomena including defocus, astigmatism, coma and sphericalaberration up to higher aberrations. In an embodiment of the presentmethod, the corneal surface measurement results in that a cornealsurface is expressed as a linear combination of the first 15 Zernikepolynomials. By means of a raytracing method, the Zernike descriptioncan be transformed to a resulting wavefront (as described in Equation(1)), wherein Z_(i) is the i-th Zernike term and a_(i) is the weightingcoefficient for this term. Zernike polynomials are a set of completeorthogonal polynomials defined on a unit circle. Below, Table 1 showsthe first 15 Zernike terms and the aberrations each term signifies.$\begin{matrix}{{z\left( {\rho,\theta} \right)} = {\sum\limits_{i = 1}^{15}\quad {a_{i}Z_{i}}}} & (1)\end{matrix}$

[0024] In equation (1), ρ and θ represent the normalized radius and theazimuth angle, respectively. TABLE 1 i Z_(i)(ρ, θ 1 1 Piston 2 2ρcosθTilt x 3 2ρsinθ Tilt y 4 $\sqrt{3}\left( {{2\rho^{2}} - 1} \right)$

Defocus 5$\sqrt{6}\left( {\rho^{2}\sin \quad 2\quad \theta} \right)$

Astigmatism 1^(st) order (45°) 6$\sqrt{6}\left( {\rho^{2}\cos \quad 2\quad \theta} \right)$

Astigmatism 1^(st) order (0°) 7$\sqrt{8}\left( {{3\quad \rho^{3}} - {2\quad \rho}} \right)\quad \sin \quad \theta$

Coma y 8$\sqrt{8}\left( {{3\quad \rho^{3}} - {2\quad \rho}} \right)\cos \quad \theta$

Coma x 9$\sqrt{8}\left( {\rho^{3}\sin \quad 3\quad \theta} \right)$

Trifoil 30° 10$\sqrt{8}\left( {\rho^{3}\cos \quad 3\quad \theta} \right)$

Trifoil 0° 11$\sqrt{5}\left( {{6\quad \rho^{4}} - {6\quad \rho^{2}} + 1} \right)$

Spherical aberration 12$\sqrt{10}\left( {{4\quad \rho^{4}} - {3\rho^{2}}} \right)\cos \quad 2\quad \theta$

Astigmatism 2^(nd) order (0°) 13$\sqrt{10}\left( {{4\quad \rho^{4}} - {3\quad \rho^{2}}} \right)\sin \quad 2\quad \theta$

Astigmatism 2^(nd) order (45°) 14$\sqrt{10}\left( {\rho^{4}\cos \quad 4\quad \theta} \right)$

Tetrafoil 0° 15$\sqrt{10}\left( {\rho^{4}\sin \quad 4\quad \theta} \right)$

Tetrafoil 22.5°

[0025] Conventional optical correction with intraocular lenses will onlycomply with the fourth term of an optical system comprising the eye withan implanted lens. Glasses, contact lenses and some special intra ocularlenses provided with correction for astigmatism can further comply withterms five and six and substantially reducing Zernike polynomialsreferring to astigmatism.

[0026] The inventive method further includes to calculate the wavefrontaberrations resulting from an optical system comprising said modeledintraocular lens and cornea and expressing it in a linear combination ofpolynomials and to determine if the intraocular lens has providedsufficient reduction in wavefront aberrations. If the reduction inwavefront aberrations is found to be insufficient, the lens will bere-modeled until one or several of the polynomial terms are sufficientlyreduced. Remodeling the lens means that at least one lens designparameter is changed. These include the anterior surface shape andcentral radius, the posterior surface shape and central radius, thethickness of the lens and its refractive index. Typically, suchremodeling includes changing the shape of a lens surface so it deviatesfrom being a spherical. There are several tools available in lens designthat are useful to employ with the design method, such as OSLO version 5see Program Reference, Chapter 4, Sinclair Optics 1996. The format ofthe Zernike polynomials associated with this application are listed inTable 1.

[0027] According to a preferred aspect of the first embodiment, theinventive method comprises expressing at least one corneal surface as alinear combination of Zernike polynomials and thereby determining theresulting corneal wavefront Zernike coefficients, i.e. the coefficientof each of the individual Zernike polynomials that is selected forconsideration. The lens is then modeled so that an optical systemcomprising of said model lens and cornea provides a wavefront having asufficient reduction of selected Zernike coefficients. The method canoptionally be refined with the further steps of calculating the Zernikecoefficients of the Zernike polynomials representing a wavefrontresulting from an optical system comprising the modeled intraocular lensand cornea and determining if the lens has provided a sufficientreduction of the wavefront Zernike coefficients of the optical system ofcornea and lens; and optionally re-modeling said lens until a sufficientreduction in said coefficients is obtained. Preferably, in this aspectthe method considers Zernike polynomials up to the 4th order and aims tosufficiently reduce Zernike coefficients referring to sphericalaberration and/or astigmatism terms. It is particularly preferable tosufficiently reduce the 11th Zernike coefficient of a wavefront frontfrom an optical system comprising cornea and said modeled intraocularlens, so as to obtain an eye sufficiently free from sphericalaberration. Alternatively, the design method can also include reducinghigher order aberrations and thereby aiming to reduce Zernikecoefficients of higher order aberration terms than the 4^(th) order.

[0028] When designing lenses based on corneal characteristics from aselected population, preferably the corneal surfaces of each individualare expressed in Zernike polynomials describing the surface topographyand therefrom the Zernike coefficients of the wavefront aberration aredetermined. From these results average Zernike wavefront aberrationcoefficients are calculated and employed in the design method, aiming ata sufficient reduction of selected such coefficients. In an alternativemethod according to the invention, average values of the Zernikepolynomials describing the surface topography are instead calculated andemployed in the design method. It is to be understood that the resultinglenses arriving from a design method based on average values from alarge population have the purpose of substantially improving visualquality for all users. A lens having a total elimination of a wavefrontaberration term based on an average value may consequently be lessdesirable and leave certain individuals with an inferior vision thanwith a conventional lens. For this reason, it can be suitable to reducethe selected Zernike coefficients only to certain degree of the averagevalue.

[0029] According to another approach of the inventive design method,corneal characteristics of a selected population and the resultinglinear combination of polynomials, e.g. Zernike polynomials, expressingeach individual corneal aberration can be compared in terms ofcoefficient values. From this result, a suitable value of thecoefficients is selected and employed in the inventive design method fora suitable lens. In a selected population having aberrations of the samesign such a coefficient value can typically be the lowest value withinthe selected population and the lens designed from this value wouldthereby provide improved visual quality for all individuals in the groupcompared to a conventional lens. One embodiment of the method comprisesselecting a representative group of patients and collecting cornealtopographic data for each subject in the group. The method comprisesfurther transferring said data to terms representing the corneal surfaceshape of each subject for a preset aperture size representing the pupildiameter. Thereafter a mean value of at least one corneal surface shapeterm of said group is calculated, so as to obtain at least one meancorneal surface shape term. Alternatively or complementary a mean valueof at least one to the cornea corresponding corneal wavefront aberrationterm can be calculated. The corneal wavefront aberration terms areobtained by transforming corresponding corneal surface shape terms usinga raytrace procedure. From said at least one mean corneal surface shapeterm or from said at least one mean corneal wavefront aberration term anophthalmic lens capable of reducing said at least one mean wavefrontaberration term of the optical system comprising cornea and lens isdesigned.

[0030] In one preferred embodiment of the invention the method furthercomprises designing an average corneal model for the group of peoplefrom the calculated at least one mean corneal surface shape term or fromthe at least one mean corneal wavefront aberration term. It alsocomprises checking that the designed ophthalmic lens compensatescorrectly for the at least one mean aberration term. This is done bymeasuring these specific aberration terms of a wavefront having traveledthrough the model average cornea and the lens. The lens is redesigned ifsaid at least one aberration term has not been sufficiently reduced inthe measured wavefront.

[0031] Preferably one or more surface descriptive (asphericitydescribing) constants are calculated for the lens to be designed fromthe mean corneal surface shape term or from the mean corneal wavefrontaberration terms for a predetermined radius. The spherical radius isdetermined by the refractive power of the lens.

[0032] The corneal surfaces are preferably characterized as mathematicalmodels and the resulting aberrations of the corneal surfaces arecalculated by employing the mathematical models and raytracingtechniques. An expression of the corneal wavefront aberrations isthereby obtained, i.e. the wavefront aberrations of a wavefront havingpassed such a corneal surface. Dependent on the selected mathematicalmodel different routes to calculate the corneal wavefront aberrationscan be taken. Preferably, the corneal surfaces are characterized asmathematical models in terms of a conoid of rotation or in terms ofpolynomials or a combination thereof. More preferably, the cornealsurfaces are characterized in terms of linear combinations ofpolynomials.

[0033] In one embodiment of the invention, the at least one nonsphericsurface of the lens is designed such that the lens, in the context ofthe eye, provides to a passing wavefront at least one wavefrontaberration term having substantially the same value but with oppositesign to a mean value of the same aberration term obtained from cornealmeasurements of a selected group of people, to which said patient iscategorized. Hereby a wavefront arriving from the cornea of thepatient's eye obtains a reduction in said at least one aberration termprovided by the cornea after passing said lens. The used expression ‘inthe context of the eye’ can mean both in the real eye and in a model ofan eye. In a specific embodiment of the invention, the wavefront obtainsreduced aberration terms expressed in rotationally symmetric Zerniketerms up to the fourth order. For this purpose, the surface of theophthalmic lens is designed to reduce a positive spherical aberrationterm of a passing wavefront. The consequence of this is that if thecornea is a perfect lens and thus not will give rise to any wavefrontaberration terms the ophthalmic lens will provide the optical systemcomprising the cornea and the ophthalmic lens with a negative wavefrontspherical aberration term. In this text positive spherical aberration isdefined such that a spherical surface with positive power producespositive spherical aberration. Preferably the lens is adapted tocompensate for spherical aberration and more preferably it is adapted tocompensate for at least one term of a Zernike polynomial representingthe aberration of a wavefront, preferably at least the 11^(th) Zerniketerm, see Table 1.

[0034] The selected groups of people could for example be a group ofpeople belonging to a specific age interval, a group of people who willundergo a cataract surgical operation or a group of people who haveundergone corneal surgery including but not limited to LASIK (laser insitu keratomileusis), RK (radial keratotomy) or PRK (photorefractivekeratotomy). The group could also be a group of people who have aspecific ocular disease or people who have a specific ocular opticaldefect.

[0035] The lens is also suitably provided with an optical power. This isdone according to conventional methods for the specific need of opticalcorrection of the eye. Preferably the refractive power of the lens isless than or equal to 30 diopters. An optical system considered whenmodeling the lens to compensate for aberrations typically includes theaverage cornea and said lens, but in the specific case it can alsoinclude other optical elements including the lenses of spectacles, or anartificial correction lens, such as a contact lens, a corneal inlay oran implantable correction lens depending on the individual situation.

[0036] In an especially preferred embodiment the ophthalmic lens isdesigned for people who will undergo a cataract surgery. In this case itis has been shown that the average cornea from such a population isrepresented by a prolate surface following the formula:$z = {\frac{\left( {1/R} \right)r^{\quad 2}}{1 + \sqrt{1 - {\left( \frac{1}{R} \right)^{2}\left( {{c\quad c} + 1} \right){r\quad}^{2}}}} + {a\quad d\quad r^{\quad 4}} + {a\quad e\quad r^{\quad 6}}}$

[0037] wherein,

[0038] (i) the conical constant cc has a value ranging between −1 and 0

[0039] (ii) R is the central lens radius and

[0040] (iii) ad and ae are aspheric polynomial coefficients additionalto the conical constant.

[0041] In these studies the conic constant of the prolate surface rangesbetween about −0.05 for an aperture size (pupillary diameter) of 4 mm toabout −0.18 for an aperture size of 7 mm. Accordingly an ophthalmic lenssuitable to improve visual quality by reducing at least sphericalaberration for a cataract patient based on an average corneal value willhave a prolate surface following the formula above. Since corneagenerally produces a positive spherical aberration to a wavefront in theeye, an ophthalmic lens for implantation into the eye will have negativespherical aberration terms while following the mentioned prolate curve.As will discussed in more detail in the exemplifying part of thespecification, it has been found that an intraocular lens that cancorrect for 100% of a mean spherical aberration has a conical constant(cc) with a value of less than 0 (representing a modified conoidsurface), with an exact value dependent on the design pupillary diameterand the selected refractive power. For example, a 6 mm diameter aperturewill provide a 22 diopter lens with conical constant value of about−1.03. In this embodiment, the ophthalmic lens is designed to balancethe spherical aberration of a cornea that has a Zernike polynomialcoefficient representing spherical aberration of the wavefrontaberration with a value in the interval from 0.000156 mm to 0.001948 mmfor a 3mm aperture radius, 0.000036 mm to 0.000448 mm for a 2 mmaperture radius, 0.0001039 mm to 0.0009359 mm for a 2,5 mm apertureradius and 0.000194 mm to 0.00365 mm for a 3,5 mm aperture radius usingpolynomials expressed in OSLO format. These values were calculated for amodel cornea having a single surface with a refractive index of thecornea of 1.3375. It is possible to use optically equivalent modelformats of the cornea without departing from the scope of the invention.For example multiple surface corneas or corneas with differentrefractive indices could be used. The lower values in the intervals arehere equal to the measured average value for that specific apertureradius minus one standard deviation. The higher values are equal to themeasured average value for each specific aperture radius plus threestandard deviations. The used average values and standard deviations areshown in tables 8,9,10 and 11. The reason for selecting only minus oneSD (=Standard Deviation) while selecting plus three SD is that in thisembodiment it is convenient to only compensate for positive cornealspherical aberration and more than minus one SD added to the averagevalue would give a negative corneal spherical aberration.

[0042] According to one embodiment of the invention the method furthercomprises the steps of measuring the at least one wavefront aberrationterm of one specific patient's cornea and determining if the selectedgroup corresponding to this patient is representative for this specificpatient. If this is the case the selected lens is implanted and if thisis not the case a lens from another group is implanted or an individuallens for this patient is designed using this patients cornealdescription as a design cornea. These method steps are preferred sincethen patients with extreme aberration values of their cornea can begiven special treatments.

[0043] According to another embodiment, the present invention isdirected to the selection of an intraocular lens of refractive power,suitable for the desired optical correction that the patient needs, froma plurality of lenses having the same power but different aberrations.The selection method is similarly conducted to what has been describedwith the design method and involves the characterizing of at least onecorneal surface with a mathematical model by means of which theaberrations of the corneal surface is calculated. The optical system ofthe selected lens and the corneal model is then evaluated so as toconsider if sufficient reduction in aberrations is accomplished bycalculating the aberrations of a wavefront arriving from such a system.If an insufficient correction is found a new lens is selected, havingthe same power, but different aberrations. The mathematical modelsemployed herein are similar to those described above and the samecharacterization methods of the corneal surfaces can be employed.

[0044] Preferably, the aberrations determined in the selection areexpressed as linear combinations of Zernike polynomials and the Zernikecoefficients of the resulting optical system comprising the model corneaand the selected lens are calculated. From the coefficient values of thesystem, it can be determined if the intraocular lens has sufficientlybalanced the corneal aberration terms, as described by the Zernikecoefficients of the optical system. If no sufficient reduction of thedesired individual coefficients are found these steps can be iterativelyrepeated by selecting a new lens of the same power but with differentaberrations, until a lens capable of sufficiently reducing theaberrations of the optical system is found. Preferably at least 15Zernike polynomials up to the 4^(th) order are determined. If it isregarded as sufficient to correct for spherical aberration, only thespherical aberration terms of the Zernike polynomials for the opticalsystem of cornea and intraocular lens are corrected. It is to beunderstood that the intraocular lens shall be selected so a selection ofthese terms become sufficiently small for the optical system comprisinglens and cornea. In accordance with the present invention, the 11^(th)Zernike coefficient, a₁₁, can be substantially eliminated or broughtsufficiently close to zero. This is a prerequisite to obtain anintraocular lens that sufficiently reduces the spherical aberration ofthe eye. The inventive method can be employed to correct for other typesof aberrations than spherical aberration by considering other Zernikecoefficients in an identical manner, for example those signifyingastigmatism, coma and higher order aberrations. Also higher orderaberrations can be corrected dependent on the number of Zernikepolynomials elected to be a part of the modeling, in which case a lenscan be selected capable of correcting for higher order aberrations thanthe 4^(th) order.

[0045] According to one important aspect, the selection method involvesselecting lenses from a kit of lenses having lenses with a range ofpower and a plurality of lenses within each power having differentaberrations. In one example the lenses within each power have anteriorsurfaces with different aspherical components. If a first lens does notexhibit sufficient reduction in aberration, as expressed in suitableZernike coefficients, then a new lens of the same power, but with adifferent surface (aspheric component) is selected. The selection methodcan if necessary be iteratively repeated until the best lens is found orthe studied aberration terms are reduced below a significant borderlinevalue. In practice, the Zernike terms obtained from the cornealexamination will be directly obtained by the ophthalmic surgeon and bymeans of an algorithm they will be compared to known Zernike terms ofthe lenses in the kit. From this comparison the most suitable lens inthe kit can be found and implanted. Alternatively, the method can beconducted before cataract surgery and data from the corneal estimationis sent to a lens manufacturer for production of an individuallytailored lens.

[0046] The present invention further pertains to an intraocular lenshaving at least one nonspherical surface capable of transferring awavefront having passed through the cornea of the eye into asubstantially spherical wavefront with its center at the retina of theeye. Preferably, the wavefront is substantially spherical with respectto aberration terms expressed in rotationally symmetric Zernike terms upto the fourth order.

[0047] In accordance with an especially preferred embodiment, theinvention relates to an intraocular lens, which has at least onesurface, when expressed as a linear combination of Zernike polynomialterms using the normalized format, that has a negative 11^(th) term ofthe fourth order with a Zernike coefficient a₁₁ that that can balance apositive such term of the cornea, to obtain sufficient reduction of thespherical aberration of the eye after implantation. In one aspect ofthis embodiment, the Zernike coefficient a₁₁ of the lens is determinedso as to compensate for an average value resulting from a sufficientnumber of estimations of the Zernike coefficient a₁₁ in several corneas.In another aspect, the Zernike coefficient a₁₁ is determined tocompensate for the individual corneal coefficient of one patient. Thelens can accordingly be tailored for an individual with high precision.

[0048] The invention further relates to another method of providing apatient with an intraocular lens, which at least partly compensates forthe aberrations of the eye. This method comprises removing the naturallens from the eye. Surgically removing the impaired lens can beperformed by using a conventional phacoemulsification method. The methodfurther comprises measuring the aberrations of the aphakic eye, notcomprising a lens, by using a wavefront sensor. Suitable methods forwavefront measurements are found in J.Opt.Soc.Am., 1994, Vol. 11(7), pp.1949-57 by Liang et. al. Furthermore, the method comprises selectingfrom a kit of lenses a lens that at least partly compensates for themeasured aberrations and implanting said lens into the eye. The kit oflenses comprises lenses of different power and different aberrations andfinding the most suitable lens can be performed in a manner as earlierdiscussed. Alternatively, an individually designed lens for the patientcan be designed based on the wavefront analysis of the aphakic eye forsubsequent implantation. This method is advantageous, since notopographical measurements of the cornea are and the whole cornea,including the front and back surfaces, is automatically considered.

[0049] The lenses according to the present invention can be manufacturedwith conventional methods. In one embodiment they are made from soft,resilient material, such as silicones or hydrogels. Examples of suchmaterials suitable for foldable intraocular lenses are found in U.S.Pat. No. 5,444,106 or in U.S. Pat. No. 5,236,970. Manufacturing ofnonspherical silicone lenses or other foldable lenses can be performedaccording to U.S. Pat. No. 6,007,747. Alternatively, the lensesaccording to the present invention can be made of a more rigid material,such as poly(methyl)methacrylate. The skilled person can readilyidentify alternative materials and manufacturing methods, which will besuitable to employ to produce the inventive aberration reducing lenses.

DETAILED DESCRIPTION OF THE INVENTION

[0050]FIG. 1 shows a comparison of the a₁₁ (“Z11”) Zernike coefficientvalues for 10 subjects if implanted with CeeOn® 911 lenses and theinventive averaged (“Z11”) lens.

[0051]FIG. 2 shows modeled visual acuities of the test subjects withCeeOn® 911 lenses and the inventive averaged (“Z11”) lenses.

[0052]FIG. 3 and FIG. 4 show modulation transfer function comparisonsbetween CeeOn® 911 lenses and the inventive averaged (“Z11”) lenses

[0053]FIG. 5 shows visual acuity plotted as a function of theastigmatism of the lenses according to the model lenses according to theinvention.

[0054]FIG. 6 shows the best corrected visual acuity with the inventivelenses.

[0055]FIG. 7 and 8 show modulation transfer functions of an individualwith an individually designed lens.

[0056]FIG. 9 shows the best corrected visual acuity with individuallydesigned lenses according to the invention.

[0057]FIG. 10 shows the age distribution of 71 patients used in a studydescribed below in the example part.

[0058]FIG. 11 shows a height map given by an Orbscan® true height datafile.

[0059]FIG. 12 shows average corneal wavefront aberration coefficients.

[0060]FIG. 13 shows a scatter plot of the spherical aberration of 71subjects for a 6 mm diameter aperture.

[0061]FIG. 14 shows a scatter plot of the spherical aberration of 71subjects for a 4 mm diameter aperture.

[0062]FIG. 15 shows a scatter plot of the spherical aberration of 71subjects for a 5 mm diameter aperture.

[0063]FIG. 16 shows a scatter plot of the spherical aberration of 71subjects for a 7 mm diameter aperture.

EXAMPLE 1

[0064] A sample set of 10 corneal surfaces from individuals weredescribed using Zernike polynomials. The sag data of the corneas wasdetermined using the real height data measured with a Humphrey Atlascorneal topographer. The corneal topographer measures the height (z_(i))at a discrete number of points. The corneal surface can then beexpressed as a linear combination of the first 15 Zernike polynomials(as described in Equation 1, above), where Z_(i) is the ith Zernikepolynomial and a_(i) is the weighting coefficient for this polynomial.The Zernike polynomials are a set of complete orthogonal polynomialsdefined on a unit circle. These polynomials as listed in Table 1 aboveand the weighting coefficients (a_(i)) are calculated from the heightdata using a Grahm-Schmidt orthogonalization procedure. The Zernikecoefficients (a_(i)) for the 10 sample corneas are listed in Table 2 inmm. TABLE 2 The Zernike coefficients for the 10 individual cornealsurfaces in mm. ACH ASA CGR CNR FCA FCM FCZ FGP JAE JBH a1 −7.713337−6.698643 −7.222353 −7.169027 −7.001356 −7.322624 −7.03713 −7.84427−7.582005 −6.890056 a2 0.000271 −0.000985 0.000386 −0.000519 0.000426−0.000094 −0.000236 −0.00056 −0.000344 −0.000155 a3 0.000478 −0.000002−0.000847 0.000996 −0.000393 0.000045 0.000454 0.000347 0.000246−0.000558 a4 0.073309 0.083878 0.077961 0.078146 0.080111 0.0777890.079987 0.072595 0.075803 0.081415 a5 −0.000316 −0.000753 0.0001190.000347 −0.001197 0.00022 −0.000071 0.000686 −0.000388 −0.000269 a60.001661 0.000411 −0.000148 −0.000386 0.000314 0.000669 0.00079 −0.000480.001688 0.001492 a7 0.000193 0.00006 −0.000295 0.000324 −0.000161−0.000058 0.000148 0.00014 0.000104 −0.000227 a8 0.000098 −0.0004370.000146 −0.00018 0.000147 0.000039 −0.000076 −0.00025 −0.000173−0.000116 a9 −0.000091 −0.000168 −0.000107 0.000047 −0.000181 −0.000154−0.000043 0.000092 −0.000023 −0.000109 a10 −0.000055 0.000139 −0.000132−0.000149 0.000234 −0.000228 0.000244 −8.2E−05 −0.000004 0.000065 a110.000277 0.000394 0.000203 0.000305 0.000285 0.000315 0.000213 0.0003080.000309 0.0004 a12 −0.000019 −0.000105 0.000025 0.00007 −0.000058−0.000033 0.00009 −2E−06 −0.000115 −0.00011 a13 0.000048 0.0000320.000085 0.000017 0.000039 0.000059 0.000022 0.000101 −0.000042−0.000052 a14 −0.000067 0.000041 −0.000081 −0.000049 0.000118 −0.0001080.000127 −1.9E−05 −0.000068 0.00001 a15 −0.000048 −0.000075 −0.000073−0.000019 −0.000036 −0.000119 −0.000021 0.000022 −0.000013 −0.000048

[0065] These wavefront aberration coefficients can be calculated usingoptical design software such as OSLO (Sinclair Optics). Table 3 showsthe results of calculating the wavefront aberration for subject FCM.(N.B. The normalization factor for the polynomials used in OSLO isdifferent from those shown in Table 3. This difference has beenincorporated into the coefficient values.) TABLE 3 The cornealaberration coefficients in mm calculated for subject FCM using OSLO(N.B.OSLO numbering order) Aberration Coefficients for FCM (OSLO) A0−0.000123 A1 4.5960e−07 A2 2.0869e−07 A3 −5.355e−06 A4 0.000551 A50.000182 A6 3.7296e−05 A7 −5.5286e−05 A8 0.000116 A9 −0.000217 A10−0.000147 A11 −3.8151e−05 A12 6.1808e−05 A13 −3.3056e−07 A14 4.888e−07A15 −1.8642e−06 A16 −0.000115 A17 −0.000127

EXAMPLE 2

[0066] An averaged design embodiment of the inventive lenses has beencalculated using the average “old” cornea information provided by PabloArtal, Murcia, Spain. This data was taken from a population sample of 16old corneas in which all of the subjects had a visual acuity of 20/30 orbetter. The corneal surfaces were described using Zernike polynomialsfor an aperture of 2.0 mm radius (r_(o)). The polynomial coefficientswere then used to determine the radius and asphericity values usingEquations 2 and 3. $\begin{matrix}{R = \frac{r_{o}^{\quad 2}}{2\left( {{2\sqrt{3}a_{4}} - {6\sqrt{5}a_{11}}} \right)}} & (2) \\{K^{2} = {\frac{8R^{3}}{r_{o}^{\quad 4}}6\sqrt{5}a_{11}}} & (3)\end{matrix}$

[0067] Note that the asphericity constant, K, describes the surface'svariation from a sphere (K²=1−e²). (i.e. For a sphere K=1 and for aparabola K=0). (cc=K²−1, wherein cc is the conical constant)

[0068] Because the cornea surface has only been described for a centraldiameter of 4 mm, the calculated R and K are also only accurate over thecentral 4 mm. A pupil size of 4.0 mm is therefore selected for designpurposes. This pupil size is reasonable for intraocular lens designpurposes.

[0069] A 22D CeeOn® 911 lens from Pharmacia Corp was chosen as astarting point for the averaged lens design. For the purpose ofcomparison, the averaged lenses were also designed to be 22D. (Note thatother dioptres would give similar simulation results, provided that thespherical surfaces of the lenses is the same.) The surface informationfor the starting point eye model is summarized in Table 4. In theconical and aspherical data demonstrated in Table 4, the average conicconstant CC is determined for the 10 individual corneas of Example 1.TABLE 4 Surface data for the starting point of the averaged (“Z11”)design Radius Thickness Aperture Conic Refractive Surface # (mm) (mm)Radius (mm) Constant Index Object — ∞ 2.272611 1.0 1 7.573 3.6 2.272611−0.0784* 1.3375 (cornea) 2 (pupil) — — 2.0 — 1.3375 3 — 0.9 2.0 — 1.33754 (lens 11.043 1.14 3.0 — 1.4577 1) 5 (lens −11.043 17.2097 3.0 — 1.3362)

[0070] The wavefront aberration coefficients in mm for the averagecornea are shown in column 1 of Table 5, while the coefficients in mm ofthe combination of the average cornea and the 911 lens are shown incolumn 2 of Table 5. Note that the Z11coefficient (a11) of the averageold cornea alone is 0.000220 mm, while the Z11of this eye implanted witha 911 would be 0.000345 mm. TABLE 5 Zernike coefficients in mm of theaverage cornea and the starting point for design (Average cornea + 911)Average Cornea Average Cornea + 911 a1 0.000432 0.000670 a2 0.0 0.0 a30.0 0.0 a4 0.000650 0.00101 a5 0.0 0.0 a6 0.0 0.0 a7 0.0 0.0 a8 0.0 0.0a9 0.0 0.0 a10 0.0 0.0 a11 0.000220 0.000345 a12 0.0 0.0 a13 0.0 0.0 a140.0 0.0 a15 0.0 0.0

[0071] The averaged lens was optimized to minimize spherical aberration,while maintaining a 22D focal power. The lens material remained the sameas in the 22D 911 lens (HRI silicone, the refractive index of which is1.45 in 77 at 37° C . The resulting design for an equiconvex lens is Theaveraged lens was optimized to minimize spherical aberration, whilemaintaining a 22D focal power. The lens material remained the same as inthe 22D 911 lens (HRI silicone, the refractive The resulting design foran equiconvex lens is provided in Table 6. The total-eye Z11coefficientof the average cornea combined with this lens is −2.42×10⁻⁷ mm(versus0.000345 mm for the cornea plus 911 lens). TABLE 6 Surface data for thestarting point of the averaged lens design 4^(th) Order 6^(th) OrderRadius Thickness Aperture Conic Aspheric Aspheric Refractive Surface #(mm) (mm) Radius (mm) Constant Constant Constant Index Object — ∞2.272611 1.0 1 (cornea) 7.573 3.6 2.272611 −0.0784 1.3375 2 (pupil) — —2.0 — 1.3375 3 — 0.9 2.0 — 1.3375 4 (lens 1) 10.0 1.02 3.0 −2.809−0.000762 −1.805e−05 1.4577 5 (lens 2) −12.0 17.2097 3.0 — 1.336

[0072] The corneas of the 10 test subjects were combined in an opticalsystem with both the 911 and the averaged lenses. The resultingtotal-eye Z11coefficients are shown in FIG. 1. As demonstrated, in FIG.1, in each case, the absolute value of the Z11 coefficient was less whenthe Z11 lens was implanted. Because subjects CGR and FCZ have relativelylow levels of corneal spherical aberration to begin with, the total-eyespherical aberration is overcorrected in these two cases. As a result,the sign of the total spherical aberration is noticeably reversed inthese two cases, and the amount of spherical aberration is stillsignificant. In every other case, the spherical aberration of the totaleye would be essentially 0 after the implantation of a Z11 lens. Thevisual acuity of each of the 10 test subjects were calculated accordingto standard methods described in “Visual acuity modeling using opticalraytracing of schematic eyes”, Greivenkamp et al., American journal ofophthalmology, 120(2), 227-240, (1995), for the implantation of both a22D 911 lens and a 22D averaged “Z11” lens. The square wave responseswere calculated using OSLO™ and a software module was written in Matlab™to calculate the visual acuity following the above method. The resultingvisual acuities are shown in FIG. 2. Out of the 10 cases investigatedand shown in FIG. 2, eight subjects had better vision when implantedwith the averaged lens according to the present invention. In the caseswhere the visual acuity decreased their Snellen distance increased byless than 1 ft which would not show up in visual acuity testing.

[0073] To be able to assess the optical quality difference between aCeeOn® 911A and averaged lenses according to the present invention, aphysical model of the average cornea was designed and manufactured. Itis a convex-plano lens of PMMA with an aspheric front surface having avalue of 0.000218 for Zernike coefficient a11. This value is almostequal to the value of the calculated average cornea: 0.000220. With thePMMA model cornea MTF measurements were performed on an optical bench ina model eye with the “averaged” Z₁₁ lenses and CeeOn® 911A lenses.Modulation Transfer Function (MTF) measurements are a widely acceptedmethod of quantifying image quality. Through focus MTF measurements at50 c/mm and a frequency MTF curves focussed at 50 c/mm, in both caseswith a 3 mm pupil are shown in the FIG. 3 and FIG. 4, respectively forlenses with an optical power of 20D. The width of the through focus MTFat 0.2 MTF units is a measure for the depth of focus and is equal forboth lenses. The MTF curve focussed at 50 c/mm for “averaged” Z11lensesis almost diffraction limited and is better than that for CeeOn 911Alenses.

[0074] The astigmatism of the cornea and the defocus of the system canbe corrected by adjusting the Zernike coefficients of the cornea modeland the focal position of the system. When this is done and theprocedure for calculating visual acuity is repeated the results in FIG.6 are obtained. They represent a modeled best corrected visual acuity.We now see that, in all cases, after correction for astigmatism anddefocus (as in reality would be done with spectacles) the inventiveaveraged lens produces a higher best corrected visual acuity than the911 lens of the same dioptre.

EXAMPLE 3

[0075] Individually Designed Lenses:

[0076] As a potential further improvement upon the averaged lens (“Z11lenses”), an individualized lens (“I11 lenses”) was designed for each offour subject corneas employing the same design principles asdemonstrated in Example 2. The individual lenses were designed such thatthe Z11 of the lens balances the Z11 of the individual cornea. Thetotal-eye Z11 coefficients for the I11 lenses are shown in Table 7,together TABLE 7 The Z11 coefficients in mm of the model eyes with the911, Z11 and I11 lenses Subject 911 averaged individual CGR 0.000107−0.000101 −0.000004 FCZ 0.000105 −0.000100 −0.000005 JAE 0.000195−0.000016 −0.000012 JBH 0.000238 0.000037 −0.000019

[0077] with the corresponding coefficients for the 911 and the averagedlenses. Furthermore, for each of the 911, Z11 (averaged), and I11(individual) lenses, the MTF curve at best focussed at 50 c/mm and thethrough focus MTF at 50 c/mm for subject JAE are plotted below in FIGS.7 and 8. From FIGS. 7 and 8, it is seen that the MTF at 50 c/mm of eyesimplanted with the Z11 and I11 lenses is higher than the MTF of the sameeyes implanted with 911 lenses. It can also be seen that the throughfocus MTF of all of the lenses is satisfactory. The Z11 has as muchdepth of focus as the 911. However, it is also interesting to note thatthe I11 does not provide a significant improvement in either MTF orthrough focus MTF, relative to the Z11 lens.

[0078] The visual acuities of the subjects with individualized lenseshave also been calculated. FIG. 9 compares these acuities with thevisual acuity calculated for the 911 and Z11 lenses.

[0079] From FIG. 9, we see that for all 4 subjects, visual acuity isbetter for both the Z11and I11 lenses than it is for the 911 lens. Wealso see that the results with the Z11 and I11 lenses do not differsignificantly—the average cornea is relatively accurate for each of the4 test subjects.

EXAMPLE 4

[0080] The design of an ophthalmic lens, which is adapted to reduce thespherical aberration of an average cornea obtained from a group ofpeople will be described in detail here below. The lens will be calledthe Z11 lens because it compensates for the normalized 11^(th) Zerniketerm describing spherical aberration of the corneas. It was decided touse a population of potential recipients of the Z11 lens, namelycataract patients.

Description of the Population

[0081] The population included 71 cataract patients from St. Erik's eyehospital in Stockholm, Sweden. These patients were of ages ranging from35 to 94 years (as of Apr. 12, 2000). The average age of our populationwas 73.67 years. A histogram of the age of the population is shown inFIG. 10.

[0082] The corneas of the 71 subjects were measured using an Orbscan®(Orbtek, Salt Lake City) device. Orbscan® is a scanning slit-based,corneal and anterior segment topographer that measures both surfaces ofthe cornea, as well as the anterior lens surface and the iris. Eachsurface can be displayed as maps of elevation, inclination, curvature,and power.

Fitting Algorithm

[0083] The corneal elevation height data (the Cartesian locations ofpoints on the surface of the cornea) for the anterior surface wasobtained using the Orbscan®, and used as raw data for the determinationof the optical properties of the cornea. The height data from an exampleOrbscan® file is represented in FIG. 11.

[0084] The Cartesian co-ordinates representing the elevation height dataare transformed to polar co-ordinates (x,y,z→r,θ,z). In order todescribe the surface, this data is then fit to a series of polynomialsas described in Equation 1b. The coefficients (a's), or weightingfactors, for each polynomial are determined by the fitting procedureresulting in a complete description of the surface. The polynomials(Z_(i)) used are the normalized Zernike polynomials. $\begin{matrix}{{z\left( {\rho,\theta} \right)} = {\sum\limits_{i = 1}^{L}\quad {a_{i}Z_{i}}}} & \left( {1b} \right)\end{matrix}$

[0085] These polynomials are special because they are orthonormal over acontinuous unit circle. They are commonly used to describe wavefrontaberrations in the field of optics. Corneal topographers measure theelevation heights at a discrete number of points. The Zernikepolynomials are not orthogonal over a discrete set of points. However,applying an orthogonalization procedure, termed Gram-Schmidtorthogonalization, to the height data, allows the data to be fit interms of Zernike polynomials maintaining the advantages of an orthogonalfit. Sixty-six coefficients (a's) were used to fit the height dataprovided by the Orbscan® software. A Matlab™ algorithm was used in thefitting procedure. The radius and asphericity value can be approximatedfrom the Zernike coefficients (Equations 2b and 3b) and the conicconstant of the surface is simply K²−1 (from this we know that for asphere K²=1). The fitting procedure is well described in a number ofreferences. Four different articles are refereed to here: “Wavefrontfitting with discrete orthogonal polynomials in a unit radius circle”,Daniel Malacara, Optical Engineering, June 1990, Vol. 29 No. 6,“Representation of videokeratoscopic height data with Zernikepolynomials”, J. Schwiegerling, J. Greivenkamp and J. Miller, JOSA A,October 1995, Vol. 12 No. 10, “Wavefront interpretation with Zernikepolynomials” J. W. Wang and D. E. Silva, Applied Optics, May 1980, Vol.19, No. 9 and “Corneal wave aberration from videokeratography: accuracyand limitations of the procedure”, Antonio Guirao and Pablo Artal, J OptSoc Am A Opt Image Sci Vis June 2000, Vol. 17(6):955-65. $\begin{matrix}{R = \frac{r_{pupil}^{\quad 2}}{2\left( {{2\sqrt{3}a_{4}} - {6\sqrt{5}a_{11}}} \right)}} & \left( {2b} \right)\end{matrix}$

$\begin{matrix}{K_{sq} = {\frac{8R^{3}}{r_{o}^{\quad 4}}6\sqrt{5}a_{11}}} & \left( {3b} \right)\end{matrix}$

Calculation of Wavefront Aberration

[0086] Knowing the shape of the anterior corneal surface (Zernikecoefficients described above as a's), it is possible to determine thewavefront aberration contributed by this surface using a raytraceprocedure. This is described in for example “Corneal wave aberrationfrom videokeratography: accuracy and limitations of the procedure”,Antonio Guirao and Pablo Artal, J Opt Soc Am A Opt Image Sci Vis June2000, Vol. 17(6):955-65.

[0087] Results:

Average Corneal Spherical Aberration and Shape

[0088] The 71 subjects were evaluated using the criteria described abovefor a 6 mm aperture. The wavefront aberration of each subject wasdetermined after fitting the surface elevation with Zernike polynomials.FIG. 12 shows that average and standard deviation of each Zernike term(normalized format). The error bars represent ±1 standard deviation.There are three aberrations that are significantly different from zeroon average in our population. These are astigmatism (A5), coma (A9) andspherical aberration (A11). Spherical aberration is the onlyrotationally symmetric aberration, making it the only aberration thatcan be corrected with a rotationally symmetric IOL.

[0089]FIG. 13 shows a scatter plot of the value of the Zernikecoefficient (OSLO format) representing spherical aberration for each ofthe 71 subjects before cataract surgery. The solid line in the middlerepresents the average spherical aberration, while the dotted linesrepresent +1 and −1 standard deviation. Table 8 lists the average,standard deviation, maximum and minimum values for the radius, asphericconstant, spherical aberration and root mean square error. TABLE 8 theaverage, standard deviation, maximum and minimum values for the radius,aspheric constant, spherical aberration and root mean square error for a6 mm aperture. Standard Average Value Deviation Maximum Minimum R (mm)7.575 0.333 8.710 7.072 Ksq 0.927 0.407 2.563 0.0152 SA coefficient0.000604 0.000448 0.002003 −0.000616 OSLO format (in mm) RMSE 0.0000550.00000482 0.000069 0.000045

[0090] Tables 9,10 and 11 below show the corresponding results foraperture sizes of 4,5 and 7 mm respectively. FIGS. 14,15 and 16 are thecorresponding scatter plots. TABLE 9 The average, standard deviation,maximum and minimum values for the radius, aspheric constant, sphericalaberration and root mean square error using an aperture diameter of 4mm. Average Value Standard Deviation Maximum Minimum R 7.56292 0.3205268.688542 7.067694 Ksq 0.988208 0.437429 2.33501 −0.051091 SA (A110.000139 0.000103 0.00041 −0.000141 in mm) RMSE 4.52E−05 4E−06 0.0000540.000036

[0091] TABLE 10 The average, standard deviation, maximum and minimumvalues for the radius, aspheric constant, spherical aberration and rootmean square error using an aperture diameter of 5 mm. Average ValueStandard Deviation Maximum Minimum R 7.55263 0.320447 8.714704 7.09099Ksq 0.945693 0.364066 2.045412 0.044609 SA 0.00031189 0.000208 0.000793−0.000276 (A11 in mm) RMSE 4.7E−05 4.02E−06 0.000057 0.000037

[0092] TABLE 11 The average, standard deviation, maximum and minimumvalues for the radius, aspheric constant, spherical aberration and rootmean square error using an aperture diameter of 7 mm. Average ValueStandard Deviation Maximum Minimum R 7.550226 0.336632 8.679712 7.040997Ksq 0.898344 0.416806 2.655164 −0.04731 SA 0.001058 0.000864 0.003847−0.001319 (A11 in mm) RMSE 7.58E−05 1.02E−05 0.000112 0.000057

Design Cornea

[0093] One model cornea was designed and each Z11lens power was designedusing this cornea. The cornea was designed so that it had a sphericalaberration that is the same as the average calculated for thepopulation. The design cornea radii and aspheric constants are listed inTable 12 for different aperture sizes. In every case, the radius ofcurvature was taken to be the average radius determined from the Zernikefit data. The aspheric constant was varied until the sphericalaberration value of the model cornea was equal to the average sphericalaberration value for the population. TABLE 12 The design cornea radiiand aspheric constants for aperture diameters of 4, 5, 6, and 7 mm.Aperture size Radius Conic Constant (mm) (mm) (OSLO value, K² − 1) Z11Coefficient (mm) 4 7.563 −0.0505 0.000139 5 7.553 −0.1034 0.000312 67.575 −0.14135 0.000604 7 7.55 −0.1810 0.001058

[0094] As discussed previously, the 6 mm aperture diameter values areused for the design cornea. This choice enables us to design the Z11lens so that it has no spherical aberration (when measured in a systemwith this cornea) over a 5.1 mm lens diameter. The OSLO surface listingfor the Z₁₁ design cornea is listed in Table 13. The refractive index ofthe cornea is the keratometry index of 1.3375.

[0095] These values were calculated for a model cornea having a singlesurface with a refractive index of the cornea of 1.3375. It is possibleto use optically equivalent model formats of the cornea withoutdeparting from the scope of the invention. For example multiple surfacecorneas or corneas with different refractive indices could be used.TABLE 13 OSLO surface listing for the Z11 design cornea. Aperture ConicRefrac- Radius Thickness Radius Constant tive Surface # (mm) (mm) (mm)(cc) index Object — 1.0000e+20 1.0000e+14 — 1.0 1 (cornea) 7.5750003.600000 3.000003 −0.141350 1.3375 2 (pupil) — — 2.640233 — 1.3375 3 —0.900000 2.64023 — 1.3375 4 25.519444 2.550292 — 1.3375 5 2.2444e−05 —1.3375

Lens Design

[0096] Each Z11 lens was designed to balance the spherical aberration ofthe design cornea. The starting point for design was the CeeOn Edge© 911lens described in U.S. Pat. No. 5,444,106 of the same power, withmodified edge and center thickness. The lens was then placed 4.5 mm fromthe anterior corneal surface. The distance from the anterior cornealsurface is not that critical and could be varied within reasonablelimits. The surface information for the starting point eye model for the22 D lens design process is listed in Table 14. The anterior surface ofthe lens was described using the formula shown in Equation 4. Thevariables cc, ad and ae were modified to minimize the sphericalaberration. The variables are determined for an aperture size of 5.1 mmand the surface is extrapolated from these values to the opticalaperture size of 6 mm. The resulting 22D Z11 eye model is listed inTable 15. The anterior surface of this 22D lens has been modified insuch a way that the spherical aberration of the system (cornea+lens) isnow approximately equal to 0. The wavefront aberration coefficients ascalculated by OSLO for the CeeOn Edge 911 22D lens eye model and the 22DZ11 lens eye model are listed below in Table 16. Note that thecoefficient representing spherical aberration for the starting point eyemodel is 0.001005 mm for a 6 mm diameter aperture placed at the cornea,while the same coefficient for the eye model with the designed Z11 lensis −1.3399e-06 mm. The same process as described above for a 22D lenscan similarly be performed for any other lens power. $\begin{matrix}{z = {\frac{\left( {1/R} \right)r^{2}}{1 + \sqrt{1 - {\left( \frac{1}{R} \right)^{2}\left( {{c\quad c} + 1} \right)r^{\quad 2}}}} + {a\quad d\quad r^{\quad 4}} + {a\quad e\quad r^{\quad 6}}}} & (4)\end{matrix}$

TABLE 14 Surface data for the starting point averaged eye model and a22D lens Aperture Conic Radius Thickness Radius Constant RefractiveSurface # (mm) (mm) (mm) (cc) index Object — 1.0000e+20 1.0000e+14 — 1.01 (cornea) 7.575 3.600000 3.000003 −0.14135 1.3375 2 (pupil) — —2.640233 — 1.336 3 — 0.900000 2.64023 — 1.336 4 (lens) 11.043 1.1642.550191 — 1.458 5 (lens) −11.043 17.1512 2.420989 — 1.336 6 (image) 0.0−0.417847 0.058997 — —

[0097] TABLE 15 Surface data for the averaged eye model and the final22D Z11 lens Aperture Conic 4^(th) Order 6th Order Radius ThicknessRadius Constant Aspheric aspheric Refractive Surface # (mm) (mm) (mm)(cc) Constant constant index Object — 1.0e+20 1.00e+14 — 1.0 1 7.5753.60 3.00 −0.14135 1.3375 (cornea) 2 — — 2.64 — 1.336 (pupil) 3 — 0.902.64 — 1.336 4 (lens) 11.043 1.164 2.55 −1.03613 −0.000944 −1.37e−051.458 5 (lens) −11.043 17.1512 2.42 — 1.336 6 (image) — — 1.59e−05 — — ——

[0098] TABLE 16 Zernike coefficients (OSLO format) for the averagecornea and a 22D 911 lens and the average cornea and the 22D Z11 lensCoefficient Average cornea + 22D 911 Average cornea + 22D Z11 a1−0.000962 −1.896e−06 a2 0.0 0.0 a3 0.0 0.0 a4 2.3101e−05 −3.9504e−06 a50.0 0.0 a6 0.0 0.0 a7 0.0 0.0 a8 0.0 0.0 a9 0.00105 −1.3399e−06 a10 0.00.0 a11 0.0 0.0 a12 0.0 0.0 a13 0.0 0.0 a14 0.0 0.0 a15 0.0 0.0

[0099] The optical form chosen for the new Z11 design is an equiconvexlens made from a silicone with refractive index of 1.458. The sphericalaberration of an average cornea is balanced by the Z11 lens yielding asystem without spherical aberration. The front surface of the lens ismodified such that the optical path lengths of all on-axis rays withinthe design aperture are the same producing a point focus. This featurecan be achieved with many lens forms. The Z11 lens could therefore bedesigned on a convex-plano, plano-convex, non-equiconvex lens or anyother design yielding a positive lens. The Z11 concept could also beextended in order to encompass a negative lens used to correct therefractive errors of the eye. The front surface or back surface couldalso be modified to produce the needed change in optical path differencethat neutralizes the spherical aberration. There are therefore manypossible designs that would achieve the goals of the Z11 lens design.

1. A method of designing an intraocular lens capable of reducingaberrations of the eye after its implantation, comprising the steps of:(i) characterizing at least one corneal surface as a mathematical model;(ii) calculating the resulting aberrations of said corneal surface(s) byemploying said mathematical model; (iii) selecting the optical power ofthe intraocular lens; (iv) modeling an intraocular lens such that awavefront arriving from an optical system comprising said lens andcorneal model obtains reduced aberrations.
 2. A method according toclaim 1, comprising determining the resulting aberrations of saidcorneal surface(s) in a wavefront having passed said cornea.
 3. A methodaccording to claim 1, wherein said corneal surface(s) is(are)characterized in terms of a conoid of rotation.
 4. A method according toclaim 1 wherein said corneal surface(s) is(are) characterized in termsof polynomials.
 5. A method according to claim 4, wherein said cornealsurface(s) is(are) characterized in terms of a linear combination ofpolynomials.
 6. A method according to claim 1, wherein said opticalsystem further comprises complementary means for optical correction,such as spectacles or an ophthalmic correction lens.
 7. A methodaccording to claim 1, wherein estimations of corneal refractive powerand axial eye length designate the selection of lens optical power.
 8. Amethod according to claim 4, wherein an optical system comprising saidcorneal model and modeled intraocular lens provides for a wavefrontsubstantially reduced from aberrations as expressed by at least one ofsaid polynomials.
 9. A method according to claim 1, wherein modeling theintraocular lens includes selecting the anterior radius and surface ofthe lens, the posterior radius and surface of the lens, lens thicknessand refractive index of the lens.
 10. A method according to claim 9,wherein the aspheric component of the anterior surface is selected whilethe model lens has predetermined central radii, lens thickness andrefractive index.
 11. A method according to claim 1 includingcharacterizing the front corneal surface of an individual by means oftopographical measurements and expressing the corneal aberrations as acombination of polynomials.
 12. A method according to claim 11 includingcharacterizing front and rear corneal surfaces of an individual by meansof topographical measurements and expressing the total cornealaberrations as a combination of polynomials.
 13. A method according toclaim 1, including characterizing corneal surfaces of a selectedpopulation and expressing average corneal aberrations of said populationas a combination of polynomials.
 14. A method according to claim 1,comprising the further steps of: (v) calculating the aberrationsresulting from an optical system comprising said modeled intraocularlens and cornea; (vi) determining if the modeled intraocular lens hasprovided sufficient reduction in aberrations; and optionally re-modelingthe intraocular lens until a sufficient reduction is obtained.
 15. Amethod according to claim 14, wherein said aberrations are expressed asa linear combination of polynomials.
 16. A method according to claim 15,wherein the re-modeling includes modifying one or several of theanterior surface and curvature, the posterior radius and surface, lensthickness and refractive index of the lens.
 17. A method according toclaim 4 or 5, wherein said polynomials are Seidel or Zernikepolynomials.
 18. A method according to claim 17, comprising the stepsof: (i) expressing the corneal aberrations as a linear combination ofZernike polynomials; (ii) determining the corneal wavefront Zernikecoefficients; (iii) modeling the intraocular lens such that an opticalsystem comprising said model lens and cornea provides a wavefront havinga sufficient reduction of Zernike coefficients.
 19. A method accordingto claim 18, further comprising the steps of: (iv) calculating theZernike coefficients of a wavefront resulting from an optical systemcomprising the modeled intraocular lens and cornea; (v) determining ifsaid intraocular lens has provided a sufficient reduction of Zernikecoefficients; and optionally re-modeling said lens until a sufficientreduction is said coefficients are obtained.
 20. A method according toclaim 19, comprising sufficiently reducing Zernike coefficientsreferring to spherical aberration.
 21. A method according to claim 19comprising sufficiently reducing Zernike coefficients referring toaberrations above the fourth order.
 22. A method according to claim 20comprising sufficiently reducing the 11th Zernike coefficient of awavefront front from an optical system comprising cornea and saidmodeled intraocular lens, so as to obtain an eye sufficiently free fromspherical aberration.
 23. A method according to claim 19, wherein there-modeling includes modifying one or several of the anterior radius andsurface, the posterior radius and surface, lens thickness and refractiveindex of the lens.
 24. A method according to claim 23, comprisingmodifying the anterior surface of the lens until a sufficient reductionin aberrations is obtained.
 25. A method according to claim 17,comprising modeling a lens such that an optical system comprising saidmodel of intraocular lens and cornea provides reduction of spherical andcylindrical aberration terms as expressed in Seidel or Zernikepolynomials in a wave front having passed through the system.
 26. Amethod according to claim 25, obtaining a reduction in higher aberrationterms.
 27. A method according to claim 8 comprising: (i) characterizingcorneal surfaces of a selected population and expressing each cornea asa linear combination of polynomials; (ii) comparing polynomialcoefficients between individual corneas; (iii) selecting one nominalcoefficient value from an individual cornea; (iv) modeling a lens suchthat a wavefront resulting arriving from an optical system comprisingsaid lens and individual cornea sufficiently reduces said nominalcoefficient value.
 28. A method according to claim 27, wherein saidpolynomial coefficient refers to the Zernike aberration term expressingspherical aberration.
 29. A method according to claim 27, wherein saidnominal coefficient value is the lowest within the selected population.30. A method of selecting an intraocular lens that is capable ofreducing aberrations of the eye after its implantation comprising thesteps of: (i) characterizing at least one corneal surface as amathematical model; (ii) calculating the resulting aberrations of saidcorneal surfaces(s) by employing said mathematical model; (iii)selecting an intraocular lens having a suitable optical power from aplurality of lenses having the same power, but different aberrations;(iv) determining if an optical system comprising said selected lens andcorneal model sufficiently reduces the aberrations.
 31. A methodaccording to claim 30, comprising determining the resulting aberrationsof said corneal surface(s) in a wavefront having passed said cornea. 32.A method according to claim 30 further comprising the steps of: (v)calculating the aberrations of a wave front arriving from an opticalsystem of said selected lens and corneal model; (vi) determining if saidselected intraocular lens has provided a sufficient reduction inaberrations in a wavefront arriving from said optical system; andoptionally repeating steps (iii) and (iv) by selecting at least one newlens having the same optical power until finding a lens capable ofsufficiently reducing the aberrations.
 33. A method according to claim30, wherein said corneal surface(s) is(are) characterized in terms of aconoid of rotation.
 34. A method according to claim 30 wherein saidcorneal surface(s) is(are) characterized in terms of polynomials.
 35. Amethod according to claim 34, wherein said corneal surface(s) is(are)characterized in terms of a linear combination of polynomials.
 36. Amethod according to claim 30 or 32, wherein said optical system furthercomprises complementary means for optical correction, such as spectaclesor an ophthalmic correction lens.
 37. A method according to claim 30,wherein corneal refractive power and axial eye length estimationsdesignate the selection of lens optical power.
 38. A method according toclaim 34 or 35, wherein an optical system comprising said corneal modeland selected intraocular lens provides for a wavefront substantiallyreduced from aberrations as expressed by at least one of saidpolynomials.
 39. A method according to claim 30 including characterizingthe front corneal surface of an individual by means of topographicalmeasurements and expressing the corneal aberrations as a combination ofpolynomials.
 40. A method according to claim 39 including characterizingfront and rear corneal surfaces of an individual by means oftopographical measurements and expressing the total corneal aberrationsas a combination of polynomials.
 41. A method according to claim 30,including characterizing corneal surfaces of a selected population andexpressing average corneal aberrations of said population as acombination of polynomials.
 42. A method according to claim 38, whereinsaid polynomials are Seidel or Zernike polynomials.
 43. A methodaccording to claim 42, comprising the steps of: (i) expressing thecorneal aberrations as a linear combination of Zernike polynomials; (ii)determining the corneal Zernike coefficients; (iii) selecting theintraocular lens such that an optical system comprising said lens andcornea provides a wavefront having a sufficient reduction in Zernikecoefficients.
 44. A method according to claim 43, further comprising thesteps of: (iv) calculating the Zernike coefficients resulting from anoptical system comprising the modeled intraocular lens and cornea; (v)determining if said intraocular lens has provided a reduction of Zernikecoefficients; and optionally selecting a new lens until a sufficientreduction is said coefficients is obtained.
 45. A method according toclaim 43 or 44, comprising determining Zernike polynomials up to the 4thorder.
 46. A method according to claim 45 comprising sufficientlyreducing Zernike coefficients referring to spherical aberration.
 47. Amethod according to claim 46 comprising sufficiently reducing Zernikecoefficients above the fourth order.
 48. A method according to claim 46comprising sufficiently reducing the 11th Zernike coefficient of awavefront front from an optical system comprising model cornea and saidselected intraocular lens, so as to obtain an eye sufficiently free fromspherical aberration.
 49. A method according to claim 39 comprisingselecting a intraocular lens such that an optical system comprising saidintraocular lens and cornea provides reduction of spherical aberrationterms as expressed in Seidel or Zernike polynomials in a wave fronthaving passed through the system.
 50. A method according to claim 39,wherein reduction in higher aberration terms is accomplished.
 51. Amethod according to claim 30 characterized by selecting an intraocularlens from a kit comprising lenses with a suitable power range and withineach power range a plurality of lenses having different aberrations. 52.A method according to claim 51, wherein said aberrations are sphericalaberrations.
 53. A method according to claim 51, wherein said lenseswithin each power range have surfaces with different asphericcomponents.
 54. A method according to claim 53, wherein said surfacesare the anterior surfaces.
 55. A method of designing an ophthalmic lenssuitable for implantation into the eye, characterized by the steps of:selecting a representative group of patients; collecting cornealtopographic data for each subject in the group; transferring said datato terms representing the corneal surface shape of each subject for apreset aperture size; calculating a mean value of at least one cornealsurface shape term of said group, so as to obtain at least one meancorneal surface shape term and/or calculating a mean value of at leastone to the cornea corresponding corneal wavefront aberration term, eachcorneal wavefront aberration term being obtained by transformationthrough corneal surface shape terms; from said at least one mean cornealsurface shape term or from said at least one mean corneal wavefrontaberration term designing an ophthalmic lens capable of reducing said atleast one mean wavefront aberration term of the optical systemcomprising cornea and lens.
 56. Method according to claim 55,characterized in that it further comprises the steps of: designing anaverage corneal model for the group of people from the calculated atleast one mean corneal surface shape term or from the at least one meancorneal wavefront aberration term; checking that the designed ophthalmiclens compensates correctly for the at least one mean aberration term bymeasuring these specific aberration terms of a wavefront having traveledthrough the model average cornea and the lens and redesigning the lensif said at least one aberration term not has been sufficiently reducedin the measured wavefront.
 57. Method according to claim 55 or 56,characterized by calculating surface descriptive constant for the lensto be designed from the mean corneal surface shape terms or from themean corneal wavefront aberration terms for a predetermined radius. 58.Method according to any one of the claims 55-57, characterized byselecting people in a specific age interval to constitute the group ofpeople.
 59. Method according to any one of the claims 55-58,characterized by selecting people who will undergo cataract surgery toconstitute the group of people.
 60. Method according to any one of theclaims 55-59, characterized by designing the lens specifically for apatient that has undergone corneal surgery and therefor selecting peoplewho have undergone corneal surgery to constitute the group of people.61. Method according to any one of the claims 55-60, characterized byselecting people who have a specific ocular disease to constitute thegroup of people.
 62. Method according to any one of the claims 55-61,characterized by selecting people who have a specific ocular opticaldefect to constitute the group of people.
 63. Method according to anyone of the claims 55-62, characterized in that it further comprises thesteps of: measuring the at least one wavefront aberration term of onespecific patient's cornea; determining if the selected groupcorresponding to this patient is representative for this specificpatient and if this is the case implant the lens designed from theseaverage values and if this not is the case implant a lens designed fromaverage values from another group or design an individual lens for thispatient.
 64. Method according to any one of the claims 55-63,characterized by providing the lens with at least one nonspheric surfacethat reduces at least one aberration term of an incoming nonsphericwavefront.
 65. Method according to claim 64, characterized in that saidaberration term is a positive spherical aberration term.
 66. Methodaccording to any one of the claims 55-65, characterized by providing thelens with at least one nonspheric surface that reduces at least one termof a Zernike polynomial representing the aberration of an incomingnonspheric wavefront.
 67. Method according to claim 66, characterized byproviding the lens with at least one nonspheric surface that reduces the11^(th) normalized Zernike term representing the spherical aberration ofan incoming nonspheric wavefront.
 68. A method according to any ofclaims 55-67 characterized by designing a lens to reduce sphericalaberration in a wavefront arriving from an average corneal surfacehaving the formula$z = {\frac{\left( {1/R} \right)r^{\quad 2}}{1 + \sqrt{1 - {\left( \frac{1}{R} \right)^{2}\left( {{c\quad c} + 1} \right){r\quad}^{2}}}} + {a\quad d\quad r^{\quad 4}} + {a\quad e\quad r^{\quad 6}}}$

wherein the conical constant cc has a value ranging between −1 and 0, Ris the central lens radius and ad and ae are aspheric constants.
 69. Amethod according to claim 68, wherein the conical constant (cc) rangesfrom about −0.05 for an aperture size (pupillary diameter) of 4 mm toabout −0.18 for an aperture size of 7 mm.
 70. Method according to claim68, characterized by providing the lens with a surface described by amodified conoid having a conical constant (cc) less than
 0. 71. Methodaccording to any one of the claims 55-70, characterized by providing thelens with a, for the patient, suitable refractive power, thisdetermining the radius of the lens.
 72. Method according to any one ofthe claims 55-71, characterized by designing the lens to balance thespherical aberration of a cornea that has a Zernike polynomialcoefficient representing spherical aberration of the wavefrontaberration with a value in the interval from 0.000156 mm to 0.001948 mmfor a 3 mm aperture radius using polynomials expressed in OSLO format.73. Method according to any one of the claims 55-71, characterized bydesigning the lens to balance the spherical aberration of a cornea thathas a Zernike polynomial coefficient representing spherical aberrationof the wavefront aberration with a value in the interval from 0.000036mm to 0.000448 mm for a 2 mm aperture radius using polynomials expressedin OSLO format.
 74. Method according to any one of the claims 55-71,characterized by designing the lens to balance the spherical aberrationof a cornea that has a Zernike polynomial coefficient representingspherical aberration of the wavefront aberration with a value in theinterval from 0.0001039 mm to 0.0009359 mm for a 2,5 mm aperture radiususing polynomials expressed in OSLO format.
 75. Method according to anyone of the claims 55-71, characterized by designing the lens to balancethe spherical aberration of a cornea that has a Zernike polynomialcoefficient representing spherical aberration of the wavefrontaberration with a value in the interval from 0.000194 mm to 0.00365 mmfor a 3,5 mm aperture radius using polynomials expressed in OSLO format.76. An ophthalmic lens obtained in accordance with any of claims 1 to75, capable of transferring a wavefront having passed through the corneaof the eye into a substantially spherical wavefront having its center inthe retina of the eye.
 77. An ophthalmic lens capable of compensatingfor the aberrations of a corneal model designed from a suitablepopulation, such that a wavefront arriving from an optical systemcomprising said model cornea and said lens obtains substantially reducedaberrations.
 78. An ophthalmic lens according to claim 77, wherein saidcorneal model includes average aberration terms calculated fromcharacterizing individual corneas and expressing them in mathematicalterms so as to obtain individual aberration terms.
 79. An ophthalmiclens according to claim 77, wherein said aberration terms is a linearcombination of Zernike polynomials.
 80. An ophthalmic lens according toclaim 79 capable of reducing aberration terms expressed in Zernikepolynomials of said corneal model, such that a wavefront arriving froman optical system comprising said model cornea and said lens obtainssubstantially reduced spherical aberration.
 81. An ophthalmic lensaccording to claim 80 capable of reducing the 11^(th) th Zernike term ofthe 4^(th) order.
 82. An ophthalmic lens according to claim 77 being anintraocular lens.
 83. An ophthalmic lens according to claim 77 adaptedto replace the natural lens in a patient's eye, said ophthalmic lenshaving at least one nonspheric surface, this at least one nonsphericsurface being designed such that the lens, in the context of the eye,provides to a passing wavefront at least one wavefront aberration termhaving substantially the same value but with opposite sign to a meanvalue of the same aberration term obtained from corneal measurements ofa selected group of people, to which said patient is categorized, suchthat a wavefront arriving from the cornea of the patient's eye obtains areduction in said at least one aberration term provided by the corneaafter passing said lens.
 84. An ophthalmic lens according to claim 83,characterized in that the surface of the lens is designed to reduce atleast one positive aberration term of a passing wavefront.
 85. Anophthalmic lens according to claim 83 or 84, characterized in that theat least one wavefront aberration term provided to the passing wavefrontby the lens is a spherical aberration term, such that a wavefrontarriving from the cornea of the patient's eye obtains a reduction insaid spherical aberration term provided by the cornea after passing saidlens.
 86. An ophthalmic lens according to any one of the claims 83-85,characterized in that the at least one wavefront aberration termprovided to the passing wavefront by the lens is at least one term of aZernike polynomial representing the wavefront aberration of the cornea.87. An ophthalmic lens according to claim 86, characterized in that theat least one wavefront aberration term provided to the passing wavefrontby the lens is the 11th normalized Zernike term of a wavefrontaberration of the cornea.
 88. An ophthalmic lens according to any one ofthe claims 83-87, characterized in that said selected group of people isa group of people belonging to a specific age interval.
 89. Anophthalmic lens according to any one of the claims 83-88, characterizedin that the lens is adapted to be used by a patient that has undergonecorneal surgery and in that said selected group of people is a group ofpeople who have undergone corneal surgery.
 90. An ophthalmic lensaccording to any one of the claims 83-88, characterized in that saidselected group of people is a group of people who will undergo acataract surgical operation.
 91. An ophthalmic lens according to claim90 characterized in that the nonspheric surface is a modified conoidsurface having a conical constant (cc) less than zero.
 92. An ophthalmiclens according to claim 91 characterized in that that is capable ofeliminating or substantially reducing spherical aberration of awavefront in the eye or in an eye model arriving from a prolate surfacehaving the formula:$z = {\frac{\left( {1/R} \right)r^{\quad 2}}{1 + \sqrt{1 - {\left( \frac{1}{R} \right)^{2}\left( {{c\quad c} + 1} \right){r\quad}^{2}}}} + {a\quad d\quad r^{\quad 4}} + {a\quad e\quad r^{\quad 6}}}$

the conical constant cc has a value ranging between −1 and 0, R is thecentral lens radius and ad and ae are aspheric constants.
 93. Anophthalmic lens according to any one of the claims 83-92, characterizedin that the lens is provided with a, for the patient, suitablerefractive power less than or equal to 30 diopters.
 94. An ophthalmiclens according to any one of the claims 83-93, characterized in that oneof the at least one nonspheric surface of the lens is the anteriorsurface.
 95. An ophthalmic lens according to any one of the claims83-94, characterized in that one of the at least one nonspheric surfaceof the lens is the posterior surface.
 96. An ophthalmic lens accordingto any one of the claims 83-95, characterized in that the lens is madefrom a soft biocompatible material.
 97. An ophthalmic lens according toany one of the claims 83-96, characterized in that the lens is made of asilicone material.
 98. An ophthalmic lens according to claim 97,characterized in that the silicone material is characterized by arefractive index larger than or equal to 1.43 at a wavelength of 546 nm,an elongation of at least 350%, a tensile strength of at least 300 psiand a shore hardness of about 30 as measured with a Shore Type ADurometer.
 99. An ophthalmic lens according to any one of the claims83-98, characterized in that the lens is made of hydrogel.
 100. Anophthalmic lens according to any one of the claims 83-95, characterizedin that the lens is made of a rigid biocompatible material.
 101. Anophthalmic lens according to any one of the claims 83-100, characterizedin that it is designed to balance the spherical aberration of a corneathat has a Zernike polynomial coefficient representing sphericalaberration of the wavefront aberration with a value in the interval from0.000156 mm to 0.001948 mm for a 3 mm aperture radius using polynomialsexpressed in OSLO format.
 102. An ophthalmic lens according to any oneof the claims 83-100, characterized in that it is designed to balancethe spherical aberration of a cornea that has a Zernike polynomialcoefficient representing spherical aberration of the wavefrontaberration with a value in the interval from 0.000036 mm to 0.000448 mmfor a 2 mm aperture radius using polynomials expressed in OSLO format.103. An ophthalmic lens according to any one of the claims 83-100,characterized in that it is designed to balance the spherical aberrationof a cornea that has a Zernike polynomial coefficient representingspherical aberration of the wavefront aberration with a value in theinterval from 0.0001039 mm to 0.0009359 mm for a 2.5 mm aperture radiususing polynomials expressed in OSLO format.
 104. An ophthalmic lensaccording to any one of the claims 83-100, characterized in that it isdesigned to balance the spherical aberration of a cornea that has aZernike polynomial coefficient representing spherical aberration of thewavefront aberration with a value in the interval from 0.000194 mm to0.00365 mm for a 3.5 mm aperture radius using polynomials expressed inOSLO format.
 105. An ophthalmic lens having at least one nonsphericalsurface which when expressed as a linear combination of polynomial termsrepresenting its aberrations is capable of reducing similar suchaberration terms obtained in a wavefront having passed the cornea,thereby obtaining an eye sufficiently free from aberrations.
 106. A lensaccording to claim 105, wherein said nonspherical surface is theanterior surface of the lens.
 107. A lens according to claim 106,wherein said nonspherical surface is the posterior surface of the lens.108. A lens according to claim 105, being an intraocular lens.
 109. Alens according to claim 105, wherein said polynomial terms are Zernikepolynomials.
 110. A lens according to claim 109 capable of reducingpolynomial terms representing spherical aberrations and astigmatism.111. A lens according to claim 110, capable of reducing the 11^(th)Zernike polynomial term of the 4^(th) order.
 112. A lens according toclaim 105 made from a soft biocompatible material.
 113. A lens accordingto claim 105 made of silicone.
 114. A lens according to claim 105 madeof hydrogel.
 115. A lens according to claim 105 made of a rigidbiocompatible material.
 116. A method of performing visual correction ina patient by implanting an intraocular lens, which at least partlycompensates for the aberrations of the eye, comprising the steps of:removing the natural lens from the eye; measuring the aberrations of theeye not comprising the lens by using a wavefront sensor; providing alens that is capable reducing at least one aberration term as found bythe wavefront sensing; implanting the lens into the eye of the patient.117. A method according to claim 116, wherein the lens is provided byselection from a kit of lenses which includes a plurality of lenses withdifferent capacity to correct said at least one aberration term withineach diopter.
 118. A method according to claim 116, wherein the lens isprovided by designing a lens that is capable of reducing at least oneaberration term resulting from the wavefront sensing of the aphakic eye.